Haben, sein, werden
These important verbs are conjugated as follows in the present tense. These patterns should be second nature to you, as you will be using them again and again to form the other tenses and verb forms:

I go. Ich gehe.
I am going. Ich gehe.
Ich bin gehen.
I eat. Ich esse.
I am eating. Ich esse
Ich bin essen.
More details
Click here to see more details, e.g. about verbs like "arbeiten" whose stem ends in a -t, about the conjugation of the verbs "wissen" and "tun," or about how to translate the "Do" that often introduces yes/no questions in English.
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Overview of Past Tenses in German
English has all kinds of ways to express past events, and there are subtle differences in meaning between them: I went, I have gone, I was going...
German has two past tenses, which we are calling "Perfekt" and "Präteritum" in this course, and there are no differences in meaning between them. The difference is simply that "Perfekt" (the two-word-past-tense) is used in informal contexts (speaking and informal writing), and "Präteritum" (the one-word-past tense) is used in more formal writing and speaking.
Perfekt [=Perfect Tense] Two-word form:
Ich bin gegangen Informal Either form translates "I went," "I have gone" and "I was going"
Präteritum [=Narrative Past, Simple Past, Imperfect] One-word form:
Ich ging Formal
Students often wonder why the two-word form, which seems more complicated, would be informal, while the seemingly simpler one-word form is formal. It turns out that formal language is actually very often much simpler than informal language: as one example, think how much harder it would be to teach someone everything involved in saying "I ain't gonna learn no &*%#@ Präteritum" and saying "I will not learn the Präteritum."
When to use the Präteritum in speaking
The formal/informal distinction is actually not so clear-cut. You will in fact see some two-word forms in formal writing, and hear some one-word forms in informal speech. There are few clear rules regarding this. You need to know that Präteritum is usually used in speaking for the following verbs:

haben sein modal verbs: können, müssen, dürfen, mögen, wollen, sollen
hatte etc. war etc. konnte, musste, durfte, mochte, wollte, sollte etc.
For the modal verbs, the reason for this is that to form the perfect tense with a modal verb, one actually needs a double infinitive construction, which sounds awkward in speaking: it is much simpler to say "Ich musste Kenny töten" than "Ich habe Kenny töten müssen." [I realize this contradicts the argument I just made above about informal language generally being more complicated than formal language... ]
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Perfekt [Perfect Tense]
Basically, the perfect tense is formed by combining haben or sein with the past participle of the verb. So you need to know the rules for the formation of the past participle, and the rules for deciding between "haben" and "sein" as the auxiliary verb.
haben vs sein
If in doubt, use "haben." "Sein" is used if
• the verb describes motion (e.g. running, jumping, skipping, but not e.g. writing or nodding one's head, which do involve motion, but are not primarily "about" that motion) or a change of location (e.g. travelling or moving from one house to another [umziehen])
• the verb describes a change of state (e.g. waking up or falling asleep, but not sleeping itself, which is a constant state)
In addition, even if the verb describes motion, "sein" is not used if the verb has an accusative object (e.g. "Ich bin gefahren," but "Ich habe das Auto gefahren").
Exceptions
The verbs "sein," "bleiben" [=to stay], "passieren" [=to happen], "geschehen" [=to happen] and "gelingen" [=to succeed] use "sein" as their auxiliary, even though they do not really describe motion or changes of state.
Summary
The following table summarizes the main points by some contrastive examples: